The semiconductor industry is continually reducing the size of features on wafers. These features include raised profiles and trenches that have a particular height (or depth), width and shape (contour). Accurate measurement of these features is necessary to insure appropriate yields.
Technologies suitable for measuring these small periodic features (critical dimensions) are quite limited. Optical measurement technology is the most desirable since it is a non-contact technique. However, the smallest spot size of conventional optical probe beams is larger than the size of the periodic features which need to be measured.
FIG. 1 illustrates a substrate 8 having basic periodic pattern 10 formed thereon. The pattern will have a certain characteristic height (H), separation (S) and width (W). Note that in this illustration, the side walls of the structure are not vertical, so the width varies over the height of the structure. FIG. 1 also schematically indicates a probe beam spot 12 which is larger than the spacing between the individual features.
The difficulty in directly measuring such small structures has lead to the development of scatterometry techniques. These techniques have in common the fact that light reflected from the periodic structure is scattered and can be treated mathematically as light scattered from a grating. A significant effort has been made to develop metrology devices that measure and analyze light scattered from a sample in order to evaluate the periodic structure.
For example, U.S. Pat. No. 5,607,800 discloses the concept of measuring reflected (scattered) light created when a broad band probe beam interacts with a sample. The reflected light intensity as a function of wavelength is recorded for a number of reference samples having known periodic features. A test sample is then measured in a similar manner and the output is compared to the output obtained from the reference samples. The reference sample which had the closest match in optical response to the test sample would be assumed to have a periodic structure similar to the test sample.
A related approach is disclosed in U.S. Pat. No. 5,739,909. In this system, measurements from a spectroscopic ellipsometer are used to characterize periodic structures. In this approach, the change in polarization state as a function of wavelength is recorded to derive information about the periodic structure.
Additional background is disclosed in U.S. Pat. No. 5,867,276. This patent describes some early efforts which included measuring the change in intensity of a probe beam as a function of angle of incidence. Measurements at multiple angles of incidence provide a plurality of separate data points. Multiple data points are necessary to evaluate a periodic structure using a fitting algorithm. In the past, systems which took measurements at multiple angles of incidence required moving the sample or optics to vary the angle of incidence of the probe beam. More recently, the assignee herein developed an approach for obtaining scatterometry measurements at multiple angles of incidence without moving the sample or the optics. This approach is described in U.S. Pat. No. 6,429,943 issued Aug. 6, 2002.
U.S. Pat. No. 5,867,276, like the other prior art discussed above, addresses the need to obtain multiple data points by taking measurements at multiple wavelengths. This patent is also of interest with respect to its discussion of analytical approaches to determining characteristics of the periodic structure based on the multiple wavelength measurements. In general, these approaches start with a theoretical model of a periodic structure having certain attributes, including width, height and profile. Using Maxwell's equations, the response which a theoretical structure would exhibit to incident broadband light is calculated. A rigorous coupled wave theory can be used for this analysis. The results of this calculation are then compared to the measured data (actually, the normalized data). To the extent the results do not match, the theoretical model is modified and the theoretical data is calculated once again and compared to the measured data. This process is repeated iteratively until the correspondence between the calculated data and the measured data reaches an acceptable level of fitness. At this point, the characteristics of the theoretical model and the actual sample should be very similar.
The calculations discussed above are relatively complex even for the most simple models. As the models become more complex (particularly as the profiles of the walls of the features become more complex) the calculations become exceedingly long and complex. Even with today's high speed processors, the art has not developed a suitable approach for analyzing more complex structures to a highly detailed level on a real time basis. Analysis on a real time basis is very desirable so that manufacturers can immediately determine when a process is not operating correctly. The need is becoming more acute as the industry moves towards integrated metrology solutions wherein the metrology hardware is integrated directly with the process hardware.
One approach which allows a manufacturer to characterize features in real time is to create “libraries” of intensity versus wavelength plots associated with a large number of theoretical structures. This type of approach is discussed in PCT application WO 99/45340, published Sep. 10, 1999, as well as the references cited therein. In this approach, a number of possible theoretical models are created in advance of the measurement by varying the characteristics of the periodic structure. The expected optical response is calculated for each of these different structures and stored in a memory to define a library of solutions. When the test data is obtained, it is compared to the library of stored solutions to determine the best fit.
While the use of libraries does permit a relatively quick analysis to be made after the sample has been measured, it is not entirely satisfactory for a number of reasons. For example, each time a new recipe is used (which can result from any change in structure, materials or process parameters), an entirely new library must be created. Further, each library generated is unique to the metrology tool used to make the measurements. If the metrology tool is altered in any way (i.e., by replacing an optical element that alters the measurement properties of the tool), a new library must be created. In addition, the accuracy of the results is limited by the number of models stored in the library. The more models that are stored, the more accurate the result, however, the longer it will take to create the library and the longer it will take to make the comparison. The most ideal solution would be to develop a system which permitted iterative (fitting) calculations to be performed in real time and which is easily modified to account for changes in the metrology tool and the process begin monitored.
One approach to speeding up the fitting calculation can be found in U.S. Pat. No. 5,963,329. (The latter patent and the other publications cited above are all incorporated herein by reference.) This patent discloses a method of reducing the number of parameters needed to characterize the shape or profile of the periodic structure. In this approach, the structure is mathematically represented as a series of stacked slabs. The authors suggest that the structure must be divided into about 20 slabs to permit proper characterization of the structure. However, the authors note that performing an analysis with 40 variables (the width and height of 20 slabs) would be too computationally complex. Accordingly, the authors suggest reducing the complexity of the calculation by using sub-profiles and scaling factors. While such an approach achieves the goal of reducing computational complexity, it does so at the expense of limiting the accuracy of the analysis. Accordingly, it would be desirable to come up with an approach that was both highly accurate and could be performed on a real time basis.